Statistics Homework

Introduction to Statistics homework: Statistics is defined as a process of analysis and organize the data.

We learn about mean, median, mode in statistics. Mean is same as average in arithmetic. Median is the midvalue of the data. Mode is the value of the data that appears most number of times.

Statistics deals with mean, deviation, variance and standard deviation. The process of finding the mean deviation about median for a continuous frequency distribution is similar as we did for mean deviation about the mean. It is a technology to collect, manage and analyze data. In this article, Basic functions and homework problems on statistics are given.

Statistics Functions and Examples:

In statistics the mean which has the same as average in arithmetic. In statistics mean is a set of data which can be dividing the sum of all the observations by the total number of observations in the data.

Sum of observations

Mean = ------------------------------------

Number of observations

The statistic is called sample mean and used in simple random sampling.

The mean of deviation has discrete frequency distribution and Continuous frequency distribution.

The mean deviation and median for a continuous frequency distribution is similar as for mean deviation about the mean.

Median is found by arranging the data first and using the formula

If n is even,

Median = '1/2[ n/2 "th item value"+(n/2+1) "th item value"]'

If n is odd, Median = '1/2 (n+1)'th item value

Variance: In statistics the variance s2 of a random variable X and of its distribution are the theoretical counter parts of the variance s2 of a frequency distribution. In a given data set of the variance can be determined by the sum of square of each data. Here variance is represented by Var (X). The formula to solve the variance for continuous and discrete random variable distributions can be shown. In statistics variance is the term that explains how average values of the data set vary from the measured data.

s2 = ?(X - M) 2 / N

S2 = ?(X - M) 2 / N

Standard Deviation: It is an arithmetical figure of spread and variability

Ex 1 : Choose the correct for normal frequency distribution.

A. mean is same as the standard deviation

B. mean is same as the mode

C. mode is same as the median

D. mean is the same as the median

Ans: D

Ex 2 : Choose the correct variable for confounding.

A. exercise

B. mean

C. deviation

D. Occupation

Ans : A

Ex 3: The weights of 8 people in kilograms are 60, 58, 55, 72, 68, 32, 71, and 52.

Find the arithmetic mean of the weights.

Sol : sum of total number

Mean = ------------------------------

Total number

60 + 58 + 55 + 72 + 68 + 32 + 71 + 52

= -----------------------------------------------------------

8

468

= -------

8

= 58.5

Ex 4: Find the median of 29, 11, 30, 18, 24, and 14.

Sol : Arrange the data in ascending order as 11, 14, 18, 30, 24, and 29.

N = 6

Since n is even,

Median = '1/2[ n/2 "th item value"+(n/2+1) "th item value"]'

= '1/2' [6/2th item value + (6/2 + 1)th item value]

= '1/2' [3rd item value + 4th item value]

= '1/2' [18 + 30]

= '1/2' * 48

= 24

Ex 5: Find the mode of 30, 75, 80, 75, and 55.

Sol : 75 are repeated twice.

Mode = 75

Ex 6: Find the Variance of (2, 4, 3, 6, and 5).

Sol: First find the mean

Mean = '(2+3+4+6+5)/5 = 20/5=4'

(X-M) = (2-4)= -2, (3-4)= -1, (4-4)=0, (6-4) =2, (5-4) =1

Then we can find the squares of a numbers.

(X-M)2 = (-2)2 = 4, (-1) 2 = 1 , 02 = 0, 22 = 4 , 12 = 1

'sum(X-M)^2= 4+1+0+4+1=10'

Number of elements = 5 , so N= 5-1 = 4

'(sum(X-M)^2)/N = 10/4=2.5'

Here we can add the all numbers and divided by total count of numbers.

= (4 + 16 + 9 + 36 + 25) / 5

= 90 / 5

= 18

Ex 7: Find the Standard deviation of 7, 5, 10, 8, 3, and 9.

Sol:

Step 1:

Calculate the mean and deviation.

X = 7, 5, 10, 8, 3, and 9

M = (7 + 5 + 10 + 8 + 3 + 9) / 6

= 42 / 6

= 7

Step 2:

Find the sum of (X - M) 2

0 + 4 + 9 + 1 + 4 = 18

Step 3:

N = 6, the total number of values.

Find N - 1.

6 - 1 = 5

Step 4:

Locate Standard Deviation by the method.

v18 / v5 = 4.242 / 2.236

= 1.89

Homework practice problems:

1. Choose the correct for statistics is outliers.

A. mode

B. range

C. deviation

D. median

Ans : B

2. Find the arithmetic mean of the weights of 8 people in kilograms is 61, 60, 58, 71, 69, 38, 77, and 51.

Sol : 60.625

3. Find the median of 22, 15, 32, 19, 21, and 13.

Sol : 20

4. Find the mode of 30, 65, 52, 75, and 52.

Sol : 52

5. Find the Variance of (3, 6, 3, 7, and 9).

Sol: 36.8

6. Find the median of 9, 12, 26, 48, 20, and 41.

Sol: 23

Identify the Correct Statement

Introduction to identify the correct statement

In this lesson we will see how to handle multiple choice questions effectively. These questions differ from other detailed problem solving as the student is provided with choices of various answers and the student is required to identify the correct answer. Normally four to five alternatives are provided, out of which usually one is correct but occasionally some multiple choice questions will have more than one correct answer. Normally, examinations with only multiple choice questions come with time constraints and in some cases a penalty is imposed for wrong answers to avoid wild guessing. It is therefore important that this section is attempted quickly and accurately.

As said above, the success in attempting these questions will depend on the ability to identify the correct answer quickly. It might not be required to solve the problem from beginning to end. The student might have enough hints to identify the wrong choice. Some of the problems will require solving up to a stage and then eliminating the wrong answers. In some cases it will be good to try working from the alternatives given into the questions and eliminate the wrong ones.

Approaches to identify the correct statement

Main approaches

Identify and eliminate wrong alternatives

Find the range of values for the possible answer or the sign of the number etc and eliminate the alternatives that are outside the range

Try plugging the alternatives in the conditions mentioned in the problem statement and see if all the conditions are met. This will help in eliminating the wrong alternatives quickly

Let us analyze the various approaches to identify the correct statement without actually spending time to solve the problem and arrive at the final answer

Ex 1: What is the value of 'sqrt(52.4176)'

A) 6.94

B) 3,88

C) 7.86

D) 7.92

Sol: It will be extremely time consuming to actually find the square root of the number 52.4176 without a calculating device. Moreover, the chances of making a mistake in calculations are also high.

Step 1: Let us first take the integer part and then identify the perfect squares near by.

The integer part of 52.4176 is 52 and the perfect squares near by are 49 and 64.

'sqrt(49)' = 7 and 'sqrt(64)' = 8.

So 'sqrt(52.4176)' lies between 7 and 8.

Step 2: This will eliminate the first two choices. We are now left with choices 7.86 and 7.92. One of these numbers if multiplied by itself should get 52.4176.

Note, that 52.4176 ends with 6.

Step 3: So the if we try multiplying 7.92 by 7.92, the end digit will have 4 ( as 2 x 2 = 4) and not 6. So 7.92 is not the right answer. The only alternative left is 7.86 and when multiplied by itself will get a number ending with 6. This is the correct choice

Ans: (C) 7.92

The above approach will considerably save time and effort to identify the answer. Note, we identified the answer, we did not work out the answer. In multiple choice questions this approach is very important

Another approach is to work from the alternatives that satisfy the conditions in the question. This approach will be faster in many cases

Let us now try another example

Ex 2: Given b = 2a, Find the values of a,b and c if, '(21a)/(c) = (b+c+1)/(a)= (2c+5a)/(b)'

A) a= 3,b= 6,c= 7

B) a= 2,b= 4,c= 7

C) a=4,b=8, c=2

D) a=1,b=7,c=6

Sol: It will be too time consuming to solve the equations and to arrive at the values for a, b and c. It will be easier if we plug in each alternative into the conditions of the question and eliminate the ones that does not satisfy.

Step 1: First condition is b = 2a, we can easily see that alternative (D) does not satisfy this condition and can be eliminated. We are now left with (A), (B) and (C) only.

Step 2: Let us try the alternative A: '(21a)/(c) = 21*3/7' = 9 and '(b+c+1)/(a) = (6 +7+1)/(3)' = 4.67. These are not equal and hence alternate (A) is not correct

Step 3: Let us try the alternative B: '(21a)/(c) = 21 * 2/7' = 6 and '(b+c+1)/(a) = (4+7+1)/(2)' = 6 and

Step 4: '(2c+5a)/(b)= (2*7 + 5*2)/(4) = 24/4' = 6.These are all equal to 6 and hence alternate (B) is correct

Step 5: To complete let us try alternate C as well

'(21a)/(c) = 21 * 4/2' = 42 and '(b+c+1)/(a) = (8+2+1)/(4)' = 2.75. These are not equal and hence alternate (C) is not correct

Ans: (B) a= 2,b= 4,c= 7

We will look at one more approach to identify the correct statement

Let us consider another example

Ex 3 : What are the roots of the quadratic equation, 3.1x2 -2.1x - 6.9 = 0

A) 1.47, 3.30

B) 2.1, -3.6

C) -3.2, -1.8

D) 1.87, -1.19

Sol: If we solve the problem using the quadratic formula, it will take a long time as it will involve find the square root of fractional numbers etc. To identify the correct statement among the above four, this is not required either. If we use the formula connecting the roots of the quadratic equation, we can eliminate the alternatives easily

Step 1: We know Sum of roots is '-b/a'

Product of roots is 'c/a'

Step 2: If we apply this for the above equation we get

Sum of root of the equation 3.1 x2-2.1 x - 6.9 = 0 is '2.1/3.1' an dpreoduct of the root is -6.9/3.1

Step 3: The product of roots is negative. This means that we will have one root with positive sign and another with negative sign. This will eliminate alternatives (A) and (C). We now need to pick from alternatives (B) and (D)

Step 4: Sum of the roots is positive, this means that the absolute value of the positive root is higher than the negative root. This will eliminate alternative (B)

The only alternative left is (D)

Ans: (D) 1.87, -1.19

Thus we could identify the correct statement without doing any calculation

Exercise on correcting statements

Pro 1: What is the value of Sin 470?

A) 0.31

B) 0.94

C) 0.731

D) 0.26

Hint: Value of Sin 0 increases from 0 to 1 as theta moves from 0 to 90

Ans: C

Pro 2: Which of the following triplets that best forms the sides of a right angled triangle?

A) 13.1,16.7, 28.51

B) 15.2,16.7, 30.4

C) 17.8,19.6,35.7

D) 24.3,15.2,28.66

Hint: Use the principle that sum of any two sides of a triangle is greater than the third side. This will help in eliminating the alternatives

Ans: D

Pro 3 : what is the value of 6.812-3.922?

A) 28.635

B) 31.097

C) 15.637

D) 38.927

Ans: B

Variables in Statistics Tutor

Introduction :

The variable which is available in the statistics it is called as statistical variable. It is a feature that may acquire choice in adding of one group of data to which a mathematical enumerates can be allocated. Some of the variables are altitude, period, quantity of profit, region or nation of birth, grades acquired at school and category of housing, etc,. Our statistics tutor defines the different types of statistics variables and the example of these types. Our tutor helps to you to know more information about the variables in statistics.

Variables in statistics tutor:

Let us, see the different types used in statistics and the uses of these types. There two kinds of used in statistics. They are,

Statistical 1: Qualitative

Statistical 1: Quantitative

These two kinds are used for various uses based on the statistics. Also, these types are divided into number of categories and which is used to various uses.

Explanation :

Qualitative :

The qualitative variant is the initial category of variable in statistics. Qualitative variables are cannot be measured which are called as attributes.

The qualitative variable is categories into two parts:

Qualitative type 1: Nominal

Qualitative type 2: Ordinal

1. Nominal variable:

Nominal values are the qualitative that does not hold any mathematical proposition like one's sacred quantity or city or surroundings. Using this nominal it does not do any addition, subtraction, even sorted.

2. Ordinal variables:

Ordinal variable is similar to the nominal variable but it uses some logical technique can arrange the variables. For instance in school ( junior and senior).

Quantitative variables:

The next category of statistical is a quantitative. The quantitative can be measured straightly.

The quantitative is categories into two parts:

Quantitative type 1: Continuous

Quantitative type 2: Discrete

1. Continuous :

The variable that can acquire all the values from the specified sequence then it is known as continuous. That is it can take an infinite value from the higher range to lower range of the given series.

Example:

Assume the person's age. Here, age is considered as a numerical value. If the age of the person is in among 36 and 56, the outcome can be any value among 36 and 56; therefore "Age of a person "is continuous variable.

2. Discrete :

The variable that can acquire only a specific value from the given range then it is said to be discrete variable. Hence, it can take the finite number of values only.

Example:

The number of child in the family is among 4 and 6, the outcome will be only 5. That is among 4 and 6, the can take only a specified value 5; therefore, "number of child in a family" is discrete variable.

What is an Integer in Math

Introduction to an integral in math:

In mathematics, an integral is one interesting topics in number representation. Integer has a set of numbers in which includes positive numbers, negative numbers and zero. An integer contains complete entity or unit. In integer, there is no fractional parts and also no decimal numbers. Integer performs different types of arithmetic operations which are addition, subtraction, multiplication and division. Let us solve some example problems for an integer in math.

Example for an integral in math:

489, - 546, 0, 84, etc.

Different rules of an integral in math:

Different rules of an integral in math are,

Integer Addition Rules:

In addition, we use the same sign means then we add the same sign integer values and then we get the same sign integral value as result.

Positive integral + Positive integer = Positive integer

Negative integral + Negative integral = Negative integer

Otherwise, we use different signs means then we subtract the different sign integral values and then we get the largest absolute value as result.

Positive integral + Negative integral

Negative integral + Positive integer

Integer Subtraction Rules:

In subtraction, we keep the first integer as same, next we change the subtraction sign to addition and change the second integers sign into its opposite then we follow the same rule for integer addition.

Integer multiplication Rules:

Like addition rule,

Positive integral × Positive integer = Positive integer

Negative integer × Negative integral = Positive integer

Positive integral× Negative integral = Negative integral

Negative integral × Positive integral = Negative integer

Integer Division Rules:

Like multiplication,

Positive ÷ Positive = Positive

Negative ÷ Negative r = Positive

Positive integer ÷ Negative integer = Negative integer

Negative integer ÷ Positive integer = Negative integer

Example problems for an in math:

Some example problems for an integral in math are,

Example 1:

Using addition operation, simplify the given integral

842 + 384

Solution:

Given two numbers are

842 + 384

Both are positive integers and the result is also a positive numbers

Here we add 842 into 384, and we get the result

842 + 384

1226

Solution to the given two is 1226.

Example 2:

Using subtraction operation, simplify the given

958 - 575

Solution:

Given two numbers are

958 - 575

Both are two positive and the result is also a positive numbers

Here we subtract 958 into 575, and we get the result

958 - 575

383

Solution to the given two is 383.

Example 3:

Using multiplication operation, simplify the given

127 × 253

Solution:

Given two numbers are

127 × 253

Both are two positive and the result is also a positive numbers

Here we multiply 127 into 253, and then we get the result

127 × 253

32131

Solution to the given two is 32131.

Example 4:

Using division operation, simplify the given

9000 ÷ 30

Solution:

Given two numbers are

9000 ÷ 30

Both are two positive and the result is also a positive numbers

Here we divide 9000 by 30, and then we get the result

9000 ÷ 30

300

Solution to the given two integra is 300.

Example 5:

Using multiplication operation, simplify the given integral

Solution:

Given two integra numbers are

Givenintegral number has both positive integral and negative integers so; the result is a negative numbers

Here we multiply - 487 into 213, and then we get the result

Solution to the given two integra is - 103731.

Example 6:

Using addition operation, simplify the given

Solution:

Given two integra numbers are

Both are two negativeintegral so, the result is also a negative numbers

Here we add - 86 into - 252, and then we get the result

Solution to the given two integral is - 338.

Practice problems for an integral in math:

Problem 1:

156 + 845

Answer: 1001

Problem 2:

756 - 345

Answer: 411.

Problem 3:

56 × 245

Answer: 13720

Problem 4:

'9996 / 357'

Answer: 28

Problem 5:

Answer: 607

Problem 6:

Answer: - 601.

Problem 7:

Answer: - 1170

Problem 8:

' 836 / 38'

Answer: 22

Ancient Greek Mathematics

Introduction to ancient greek mathematics :

Ancient greeks are regarded as one of the major discoverer of "Geometry". The greeks were not intrested in numbers much. So they showed their interest in geometry which led to major discoveries. The notable achievements of the greek mathematicians were observed mainly in the period of 6th century BC to 4th century AD.

The word "Mathematics" was termed by pythagoreans (the followers of pythagoras) from the greek word "mathema" meaning " subject of instructions".

Major discoveries in ancient greek mathematics

Some of the major discoveries made by the ancient greek mathematicians are as follows :

The concept of theorems and postulates was introduced by the ancient greek mathematicians.

Euclid's elements were introduced.

One of the most important discovery was theory of conic sections during Hellinistic period.

Archimede's principle was introduced during this period.

Some major contributions were also made in the field of astronomy.

Other achievements were also made in number theory, applied mathematics, mathematical analysis and were close to integral calculus.

Major ancient greek mathematicians

The most famous greek mathematicians are:

Pythagoras

Pythagoras had major contributions in the field of Mathematics. He introduced pythagoras theorem and its proof. He also proved the existence of irrational numbers. He had interests in other fields such as astronomy and philosophy. His studies had a great influence on Plato. He also established an academy with an aim to spread Mathematics in the universe.

Anaxagoras

He was a pre - Socratic greek philospher. He made a significant contribution in the field of cosmology. He studied the celestial bodies closely.

Aristarchus

He was a Greek mathematician and an astronomer. He was the first astronomer to place sun at the center of the solar system instead of Earth. He proposed heliocentric model of solar system. He calculated distance of sun, moon from earth and their sizes.

Thales

He introduced Thales theorem and many corollaries which he used to calculate the height of pyramid and distance of ship from the shore.

Euclid

He introduced a book named Elements. He defined the terms theorems, proofs, postulates etc. His major contribution was conic section.

Archimedes

Archimedes gave an approximate value of Pi. He also calculated area covered by the arc of parabola and had major contribution in area of calculus. He produced the solution for infinite summation series.

Eudoxus

His contributions are observed in modern integration.

and many other greek mathematicians existed during the hellinistic period.

The origins of Greek mathematics are not easily documented. The earliest advanced civilizations in the country of Greece and in Europe were the Minoan and later Mycenean civilization, both of which flourished during the 2nd millennium BC. While these civilizations possessed writing and were capable of advanced engineering, including four-story palaces with drainage and beehive tombs, they left behind no mathematical documents.

Hydroelectric Energy Production

Hydroelectric energy production

What is Hydro electricity?

Hydro electrical energy is the term referring to electricity generated by hydro power; the production of electrical power through the use of the gravitational force of falling or flowing water. It is the most widely used form of renewable energy. Once a hydroelectric complex is constructed, the project produces no direct waste, and has a considerably lower output level of the carbon dioxide (CO2) than fossil fuel powered energy plants.

History of hydro electricity :

History of hydro electricity Hydro power has been used since ancient times to grind flour and perform others tasks. In the mid-1770s, a French engineer Bernard Forest de Belabor published Architecture Hydraulique which described vertical- and horizontal-axis hydraulic machines. In the late 1800s, the electrical generator was developed and could now be coupled with hydraulics. The growing demand for the Industrial Revolution would drive development as well. In 1878, the world's first house to be powered with hydroelectricity was Cragside in Norththumberland England. The old Schoelkopf power station No 1 near Niagara falls in the U.S. side began to produce electricity in 1881.

Methods to generate Hydro electricity :

Methods to generate Hydro electricity There are four methods to generate Hydro electricity :- Tide Pumped-storage Run-of-the-river Conventional

Conventional method :

Most hydroelectric power comes from the potential energy of dam water driving water turbine and generator. The power extracted from the water depends on the volume and on the difference in height between the source and the water's outflow. The amount of potential energy in water is proportional to the head. To deliver water to a turbine while maintaining pressure arising from the head, a large pipe called a penstock may be used . Conventional method

hydroelectric energy production-Advantages and disadvantages

Pumped storage method :

Pumped storage method This method produces electricity to supply high peak demands by moving water between reservoirs at different elevations. At times of low electrical demand, excess generation capacity is used to pump water into the higher reservoir. When there is higher demand, water is released back into the lower reservoir through a turbine. Pumped-storage schemes currently provide the most commercially important means of large-scale grid energy storage and improve the daily capacity factor of the generation system.

Tide method :

Tide method A tidal power plant makes use of the daily rise and fall of water due to tides; such sources are highly predictable, and if conditions permit construction of reservoirs, can also be dispatched to generate power during high demand periods. Less common types of hydro schemes use water's kinetic energy or undammed sources such as undershot waterwheels.

How to calculate the amount of available power :

How to calculate the amount of available power A simple formula for approximating electric power production at a hydroelectric plant is :- P= ?hrgk where P is Power in watts, ? is the density of water (~1000 kg/m3), h is height in meters, r is flow rate in cubic meters per second, g is acceleration due to gravity of 9.8 m/s2 k is a coefficient of efficiency ranging from 0 to 1. Efficiency is often higher (that is, closer to 1) with larger and more modern turbines.

Advantages :

The major advantage of hydroelectricity is elimination of the cost of fuel. The cost of operating a hydroelectric plant is nearly immune to increases in the cost of fossil fuels such as oil , natural gas or coal and no imports are needed. Since hydroelectric dams do not burn fossil fuels, they do not directly produce carbon dioxide. A hydroelectric plant may be added with relatively low construction cost, providing a useful revenue stream to offset the costs of dam operation. Advantages

Disadvantages :

Disadvantages Hydroelectric power stations that uses dams would submerge large areas of land due to the requirement of a reservoir. Changes in the amount of river flow will correlate with the amount of energy produced by a dam. Generation of hydroelectric power changes the downstream river environment. Large reservoirs required for the operation of hydroelectric power stations result in submersion of extensive areas upstream of the dams, destroying biologically rich and productive lowland and valley forests, marshland and grasslands.

How to Write a Demand Equation?

Introduction to How to write a demand equation

A demand equation shows the negative relationship between the price of the goods and quantity of the goods demanded keeping the other factors constant. When the price rises the quantity of goods demanded falls and when the price falls the quantity of goods demanded increases. A demand equation or a exact function expresses demand q (the number of items demanded) as a function of the unit price p (the price per item).

Equilibrium in the market happens at the quantity and price where exact is equal to the supply.

A simple exact equation -

For example; q = 5000 - 20P

Here, 5000 is the constant factor and it is negatively related to the price depicted by the -20P. It shows if the prices are prevailing at 100 per unit then q=5000 - 20(100) is q = 5000-2000 i.e q =3000 unit. Therefore at prices of 100 per unit, 3000 units of that item will be bought.

Writing a demand equation ;The factors affecting demand -

Prices of the product:

Prices are negatively related to the demand of the product. When prices rise demand falls and vice versa.

2. Income of the person:

Income of a person is directly related to the exact. When income rises demand for product also rises generally.

3. Prices of the substitute goods:

When prices of some substitute good increases then exact for its substitutes also increase making it more desirable among consumers. For example when prices of coke rise then the demand for Pepsi also rises.

4. Prices of complimentary goods:

When prices of the complimentary good increases then demand for its compliments also falls making it less desirable among consumers. For example when prices of petrol rises then the demand for cars falls.

5. Taste and preferences of the consumers:

Taste and preferences of the consumers keep on changing. A product demanded today may not be exact tomorrow.

The simplified form of linear demand function is,

q = mp + b

Where,

q - exact

p - Unit price

Wrting a detailed exact equation -

For example; q = 5000 - 20P + 10Y + 5Ps - 50Pc + 20T - 15T

Here, -20P = Negative relationship with prices

+10Y = Positive relationship with income

+5Ps = Positive relationship with increase in price of substitutes

-50Pc = Negative relationship with increase in price of compliments

+20T = Favourable taste and preference

-15T = Unfavourable taste and preference

Examples on exact Equation

Example: 1

The annual sales of a mobile shop have the following expression.

q = -30p + 7000

If you charge $100 per unit then find the expectation to sell.

Solution:

Given:

q = -30p + 7000

p = 100

Step 1:

The general form of linear demand function is as follows.

q = mp + b

Step 2:

q = -30(100) + 7000

= -3000 + 7000

= 4000

Answer: Linear demand function = 4000

Example: 2

The annual sales of a bag shop have the following expression.

q = -40p + 8000

If you charge $50 per unit then find the expectation to sell.

Solution:

Given:

q = -40p + 8000

p = 50

Step 1:

The general form of linear demand function is as follows.

q = mp + b

Step 2:

q = -40(50) + 8000

= -200 + 8000

= 7800

Answer: Linear demand function = 7800

Problems on exact Equation

Problem: 1

The annual sales of a bag shop have the following expression.

q = -20p + 5000

If you charge $20 per unit then find the expectation to sell.

Answer: 4600

Problem: 2

The annual sales of a mobile shop have the following expression.

q = -10p + 6000

If you charge $30 per unit then find the expectation to sell.

Answer: 5700

Number Zero Origin

THE ORIGIN OF NUMBER ZERO:-

In this Article the information about the history of zero and its importance, its usage in various cultures is discussed, in addition to that its relevance and importance in fields other than mathematics is discussed

According to Charles Seife, author of "Zero: The Biography of a Dangerous Idea", The Number zero was first used in West circa 1200; it was delivered by an Italian Mathematician, who joined this, with the Arabic numerals. For Zero there are at least two discoveries, or inventions. He says that the one was from the Fertile Crescent. That first came to existence in Babylon, between 400 to 300 B.C. Seife also says that, before 0 getting developed in India, it started in Northern Africa and from the hands of Fibonacci and to Europe Via Italy.

Zero, initially was a mere place holder, Seife says 'That is not a full zero', "A Full zero is a number on its own; It's the average of 1 and -1". "In India zero took as a shape, unlike being a punctuation number between numbers, in the 5th century A.D.", says Dr.Robert Kaplan. He is the author of "The nothing that is: A Natural History of Zero". "It isn't until then and not even full then, that Zero gets citizenship in the republic of numbers," says Kaplan.

In Mayan Culture, In the new world the second look of Zero appears then, in the centuries of A.D. Also Kaplan says, "That I suppose Zero being wholly devised form the scratch"

An Italian book mentioned a point about Zero, saying that The usage of Zero by Ellenistic Mathematicians, would have defined a decimal notation equivalent to the system used by the Indo-Arabic. The Book is titled - "La rivoluzione dimenticata - The Forgotten Revolution" Russo, 2003, Feltrinolli by Lucio Russo.

The ancient Greeks were very doubtful about zero as being a number. They kept posing questions on this topic. "How can nothing be something?", these questions led to philosophical arguments about the usage of zero. Comparing it with vacuum many discussions took place.

number zero origin - More information

More about the number zero origin:-

Zero is written as a circle or an eclipse. Earlier, there was no much difference between the letter o and 0. Type writers earlier had no distinction between o and 0. There was no special key installed on the type writer for zero. A slashed zero was used to distinguish between letter and digit. IBM used the digit zero by putting a dot in the center and this was continued in the Microsoft windows also. Another variation proposed at that time was a vertical bar instead of dot. Few fonts which were designed for the use in computer made the o letter more rounded and digit 0 more angular. Later the Germans had made a further distinction by slitting 0 on the upper right side.

number zero origin - importance

IMPORTANCE:-

The value zero is used extensively in the fields of Physics, Chemistry and also Computer Sciences. In Physics zero is distinguished form all other levels. In Kelvin Scale the coolest temperature chosen is zero. In Celsius scale zero is measured to be the freezing point of water. The intensity of sound is measured in decibels or photons, wherein zero is set as a reference value.

Zero has got very importance as all its binary coding is to be done with 1's and 0's. Before the existence of 0 the binary coding is very difficult. The concept of arrays also uses 0 prominently, for n items it contains 0 to n-1 items. Database management always starts with a base address value of zero.

Five Number Summary Online

Introduction to five number summary online help:

Five number summary is one of the important topics in mathematics. Five number summary is a sample from which they are derived from a particular group of individuals. Five number summary has a set of observations. In a single variable, it has a set of observations. Five number summary has a different statistics. Here we help learn about the different statistics involved in five number summary.

Online:

The specific meaning of the term online is nothing but the connecting two states. Online is mostly used in computer technology and telecommunications. Online can be referred the World Wide Web or it may be Internet.

Five number summary online help:

Different statistics are involved in five number summary are,

Minimum

Maximum

Median

Lower quartile

Upper quartile

Minimum:

Lowest value in the given set of numbers.

Maximum:

Largest value in the given set of numbers.

Median:

Middle value in the given set of numbers.

Lower quartile:

Number between the minimum and median.

Upper quartile:

Number between the maximum and median.

Five number summary online help - Steps to solve:

There are different steps to solve the five number summary are,

Observation can be arranged in the ascending order.

The lowest and largest value in the observation can be determined.

The median can be determined. When the observation has odd number of observation than the median is in middle of the observation. Otherwise it is an even number then the median is calculated by the average of the two middle numbers.

The upper quartile can be determined. When the observation minus one is divided by 4 means it is starting with the median and observations in the right side. Otherwise the observation is not divided by four means upper quartile is the median of the observation to the right of the location of overall median.

The lower quartile can be Determined. When the observation set minus one is divided by 4 then it is starting with the median and its observations in the left side. Otherwise the observation is not divided by four means lower quartile is the median of the observation to the left of the location of overall median

Five number summary online help - Example problem:

Example 1:

Help to find the five number summary for the given set of data

{235, 222, 244, 255, 217, 228, and 267}

Solution:

Given set of data

{235, 222, 244, 255, 217, 228, and 267}

{217, 222, 228, 235, 244, 255, 267} [Arrange the set in ascending order]

Minimum and Maximum values in the given set of data are 217 and 267.

Median:

Given observation is odd. So the median is middle of the observation then the median is 235.

Lower quartile:

Given observation is not divisible by four. So the lower quartile is {217, 222, and 228}

Upper quartile:

Given observation is not divisible by four. So the upper quartile is {244, 255, and 267}.

Answer:

Minimum: 217

Maximum: 267

Median: 235

Lower quartile: {217, 222 and 228}

Upper quartile: {244, 255 and 267}

Discrete Mathematics

Introduction to discrete mathematics pdf:

Discrete mathematics is part of 3 main topics

Mathematics Logic

Boolean Algebra

Graph Theory

discrete mathematics pdf-Mathematics Logic

The find of logic which is used in mathematics is called deductive logic. Mathematical arguments must be strictly deductive in nature. In other words, the truth of the statements to be proved must be established assuming the truth of some other statements.

For example, in geometry we deduce the statement the statement that he sum of the three angles of a triangle is 180 degrees from the statement that an external angle of a triangle is equal to the sum of the other (i.e., opposite) two angles of the triangles of the triangle.

The kind of logic which we shall use here is bi-valued i.e. every statement will have only two possibilities, either True' or 'False' but not both.

Definition:- The symbols, which are used to represent statements, are called statement letters or sentence variables.

To represent statements usually the letters P, Q, R, ..., p, q, r, ... etc., are used

discrete mathematics pdf-Boolean algebra

Boolean algebra was firstly introduced by British Mathematician George Boole (1813 - 1865).the original purpose of this algebra was to simplify logical statements and solve logic problems. In case of Boolean algebra, there are mainly three operations (i) and (ii) or and (iii) not which are denoted by '^^' ,'vv' and (~) respectively. In this chapter, we will use +, . , ' in place of above operations respectively.

Definition:-Let B be a non-empty set with two binary operations + and ., a unary operation ' and two distinct elements 0 and 1. Then B , +, . ,' is called Boolean algebra, if the following axioms are satisfied.

discrete mathematics pdf-Graph theory

Graphs appear in many areas of mathematics, physical, social, computer sciences and in many other areas. Graph theory can be applied to solve any practical problem in electrical network analysis, in circuit layout, in operations research etc.

By a graph, we always mean a linear graph because there is no such thing as a non-linear graph. Thus in our discussion we shall drop the adjective 'linear', and will say simply a 'graph'

Definition:- A graph G = (V, E) consists of a set of objects V = (v1, v2, ...), whose elements are called vertices (or points or nodes) and an another set E = {e1, e2, ....} whose elements are called edges (or lines or branches) such that each ek is identified with an unordered pair (vi, vj) of vertices. The vertices vi and vj associated with the edge ekare said to be the end vertices of ek.

Magnet Uses

Introduction to magnet uses:

Magnet is an object that produces a magnetic field. The so called magnetic field is invisible to human eye, but it solely responsible for creating the typical characteristic and property of a magnet, i.e. the invisible force that attracts other various ferromagnetic materials and objects like iron, and attracts and repels other magnets as well. There are permanent magnets that are naturally magnetized and create a consistent magnetic field around them. There are also materials that can be magnetized artificially and hence they get attracted to magnets. These are known as ferromagnetic materials and objects. Another aspect is the electro magnet. An electro magnet is made up of a coil which acts as a magnet when certain electric current passes through it. The magnetic moment determined the overall strength of a magnet while the magnetization determines the local strength of magnetism in a material.

Electro Magnets in details

In simple words, an electro magnet is made up by coiling an electric wire into number of lops called the solenoid. It is when electric current is passed through the wire; it creates a strong magnetic field around it, hence providing it the basic magnetic property of attracting ferromagnetic objects. There are a number of uses of an electro magnet. Electro magnets are used for manufacture of junkyard cranes, particle accelerators, magnetic resonance machines for detecting health problems, for manufacture of electric bells, for manufacture of magnetic locks, for magnetic separation of particles, for manufacture of MRI machines and mass spectrometers and other electro mechanical devices.

Common Uses of a Magnet

There are numerous uses of a magnet. Magnet is used in daily life and also for industrial purposes. It is dynamic and extremely resourceful. Following are some very vital uses of a magnet -

Credit Cards and Debit Cards: A wide use of magnets is in the manufacture of credit cards, debit cards and ATM cards. Behind each of these is a magnetic strip. The information is encoded in the magnetic strip and helps to contact the individual's financial institution and connect with their accounts.For manufacture of electric motors and generators: There is a combination of an electro magnet and a permanent magnet found in motors that help to convert electric energy into mechanical energy. The reverse concept is used in generators which coverts mechanical energy into electric energy.Medication: Now days the use of magnets by hospitals has increased substantially. Use of magnets has brought a revolution in the field of surgery and medication. The modern day doctors use the process of Magnetic Resonance Imaging. Through this concept, all the major problems of the patients are diagnosed by the doctors without performing any kind of invasive surgery.For magnetic recording media: Video tapes, Computer Floppies, Hard Disks and etc. use the concept of magnetic reel which helps to encode the information on the magnetic coating which ultimately is transferred in the form of audio and video. This was arguably the revolution as far as the extensive use of magnets is concerned.Miscellaneous: Other very vital uses of magnets are for manufacturing of toys, manufacturing of speakers and micro phones, industrial uses such as lifting heavy iron objects, manufacturing of transformers, for the process of manufacturing of jewellery, for manufacture of chucks that help in the field of metal working etc.Rate this Article

Nandan Nayak has published 80 articles. Article submitted on May 31, 2013. Word count: 545

"A geothermal power plant uses its geothermal activity to generate power. This type of natural energy production is extremely environmentally friendly and used in many geothermal hot spots around the globe.

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Gifted children oftentimes need more help than they can get in a regular school. If you're looking for ways to keep your kids challenged, consider schools for gifted kids. If private school isn't an option, you do have other choices.

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Why is Geometry Important in Life

Introduction:

Geometry is important in life because it is the learning of space and spatial dealings is an important and necessary area of the mathematics curriculum at every evaluation levels. The geometry theories are important in life ability in much profession. The geometry offers the student with a vehicle for ornamental logical reasoning and deductive thoughts for modeling abstract problems. The study of geometry is important in life because it's increasing the logical analysis and deductive thinking, which assists us expand both mentally and mathematically.

Definition for why is geometry important in life:

This article going to explain about why geometry is important in life. Geometry is a multifaceted science, and a lot of people do not have an everyday need for its most advanced formulas. Understanding fundamental geometry is essential for day to day life, because we never know when the capability to recognize an angle or figure out the region of a room will come in handy.

Importance of geometry in life:

The world is constructing of shape and space, and geometry is its mathematics.

It is relaxed geometry is good preparation. Students have difficulty with thought if they lack adequate experience with more tangible materials and activities.

Geometry has more applications than just inside the field itself. Often students can resolve problems from other fields more easily when they represent the problems geometrically.

Uses of geometry:

Gtry is the establishments of physical mathematics presents approximately surround us. A home, a bike and everything can made by physical constraints is geometrically formed.

Gmetry allows us to precisely compute physical seats and we can relate this to the convenience of mankind.

Anything can be manufacturing use of geometrical constraints like Architecture, design, engineering and building.

Example:

Let us see one example regarding why geometry important in our life. If you want to paint a room in your accommodation, you should know how much square feet of room you are going to cover by paint in order to know how much paint to buy. You should know how much square feet of lawn you contain to buy the correct amount of fertilizer or grass seed. If you required constructing a shed you would have to know how much lumber to buy so you should know the number of the square feet for the walls and the floor.

architecture is a one of the foundation of all technologies and science using the language of pictures, diagrams and design. was fully depends on structure ,size and shape of the object. In every day was very important in architectural through more technologies In a daily life was used in th technology of computer graphics, structural engineering, Robotics technology, Machine imaging, Architectural application and animation application.

In this article why is geometry important in architecture, We see about application of architecture in daily life and technology sides.

Basic concepts of important in architecture:

General application of or important :

Generally was used for identifying size, shape and measurement of an object.

Fining volume, surface area, area ,perimeter of the room a and also properties about shaped objects in building construction.

Also used for more technologies for example : computer graphics and CAD

Computer graphics:

In computer graphics was used to design the building with help of more software technologies. And also how to transferred the object position.

Set Builder Notation Math

Introduction to set builder notation in math:

In set theory and its applications to logic, mathematics, and computer science, builder notation (sometimes simply notation) is a mathematical notation for describing a set by stating the properties that its members must satisfy. In math, forming sets in this manner is also known as set comprehension, set abstraction or as defining a set's intension. (Source: From Wikipedia).

Explanation of builder notation in math:

The common property of st should be such that it should specify the objects of the lay only. For example, let us consider the lay {6, 36, 216}.

The elements of the st are 6, 36 and 216. These numbers have a common property that they are powers of 6. So the condition x = 6n, where n = 1, 2 and 3 yields the numbers 6, 36 and 216. No other number can be obtained from the condition.

Thus we observe that the set {6, 36, 216} is the collection of all numbers x such that x = 6n, where n = 1, 2, 3. This fact is written in the following form {x | x = 6n, n = 1, 2, 3}. In words, we read it as the lay consisting of all x such that x = 6n, where n = 1, 2, 3.

Here also, the braces { } are used to mean 'the consisting of '. The vertical bar ' | ' within the braces is used to mean 'such that '. The common property 'x = 6n, where n = 1, 2 and 3 acts as a builder for the lay and hence this representation is called the set-builder or rule form.

If P is the common property overcome by each object of a given st B and no object other than these objects possesses the property P, then the st B is represented by { x | x has the property P} and we say that B is the of all elements x such that x has property P.

Problems in set builder notation:

Example problem 1:

Represent the following in builder notation:

(i) The set of all natural numbers less than 8.

(ii) The set of the numbers 2, 4, 6, ... .

Solution:

(i) A natural number is less than 8 can be described by the statement:

x ? N, x < 8.

Therefore, the lay is {x | x ? N, x < 8}.

(ii) A number x in the form of 2, 4, 6, ... can be described by the statement:

x = 2n, n ? N.

Therefore, the lay is {x | x = 2n, n ? N}.

Example problem 2:

Find the lay of all even numbers less than 28, express this in lay builder notation.

Solution:

The lay of all even numbers less than 28.

The numbers are, x = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26}

{x | x is a even number, x < 28}.

Equalative Fraction

Introduction to equalative fraction:

The equivalent fraction, multiplying the numerator and denominator of a fn by the same (non-zero) number, the results of the new fraction is said to be equivalent to the original fraction. The word equivalent means that the two fns have the same value. (Source: Wikipedia)

Before the introduction of the decimal system children need to learn a lot more about fractions, as this was the only way to show a part of a whole number. In the past, using such as 5/2 and 3/5 to describe shares of objects or groups of objects was common. These have been replaced by decimals and the calculations are frequently done and writing is done in a different way to whole numbers.

A fraction consists of numerator and a denominator. This area of mathematics has frequently caused problems for both teachers and students alike, this concern however, is unnecessary if the correct grounding is given and basic concepts are understood.

Equalative fraction - Definition and examples:

Definition for equivalent :

The equivalent frs are fractions that are equal to the each other. We can use cross multiplication to decide to whether two fs are equivalent. The fractions that explain the same amount are called equivalent fs.

The equivalent frs of the same value or equivalent means equal in value. Fraction can look different but be equivalent. These fs are really the same,

Example: 3/4 = 15/20 = 75/100

The rule for equivalent multiplying numerator and denominator of a derived by the same number or a whole fraction, the results of derived is said to be equivalent to the original fraction. The equivalent fraction that two derived values have, the same value and they retain of the same integrity and proportion.

Equalative fraction:

Two frs are equivalent frs if they have the same value. The common denominator is add and subtract fn each derived must have a common denominator they must be same thing. In derived we must find a number that all the denominators will divide evenly into, Example look at the derived 1 / 4 and 1 / 6 .The denominators for these fractions are 4 and 6. A number that 4 and 6 will divide into evenly is 24.

Equalative fn - Example problems:

3 / 4 = 15 / 206 / 7 = 24 / 288 / 10 = 16 / 206 / 8 = 18 / 245 / 7 = 25 / 357 / 8 = 28 / 32

Simplify the equalative and examples:

Simplify the equalative :

A fraction is in simplest method, if the numerator and the denominator are relatively prime numbers. The concept of simplifying derived is obviously connected to the concept of equivalent fractions. One main connection is that when we are simplifying derived, we are basically finding an equivalent fraction in which the numerator and denominator are smaller (and thus simpler) numbers.

The equivalent makes simpler a derived we find a number which will divide into both the numerator and the denominator evenly, leaving no remainder. Example, to simplify the fraction 35 / 20 we divide the numerator and denominator by 5. So, 7 / 4 is the simplified derived for 35 / 20

Equalative fraction - Example problems:

15 / 30 = 3 / 10

25 / 35 = 5 / 7

27 / 36 = 9 / 12

32 / 28 = 8 / 7

45 / 40 = 9 / 8

22 / 14 = 11 / 7

Tips to Maintain Better Grades In School

One of the more stressful things that you are likely to face in your school career is trying to keep your grades at acceptable levels. Ultimately, this is something that you have control over, although you are going to need to work hard in order to get the highest grades that are possible. If you find that you are struggling in this regard or if you would simply like to do your very best academically, here are some tips that can help you to get those good grades that you desire.

One important thing for you to consider that is often overlooked by students is the position within the classroom where you are sitting. If you tend to gravitate toward the edges or the back of the class, it is likely that you are going to have lower grades as a result. This is not only because of the fact that you will miss out on some of the one-on-one attention that you can get from the teacher, it is also because of the distractions that may take you away from your courses. In addition, seating yourself in the front of the classroom in a position where you are close to the teacher is also going to let them know that you are serious about your school career.

Do you know how to study properly? This is something that many students struggle with but it is one of the more important things that must be mastered. You should work on your study skills and continue to study on a daily basis. Take notes while you're in class and review those notes as a form of studying which will help you to keep everything fresh in mind. If you find that your mind is drifting during the time that you should be studying, try to block your time in small increments so that you can remain focused.

Have you considered the possibility of hiring a tutor? Tutoring is possible for almost any subject, from hiring a math tutor online for kids all the way to getting more specific tutoring for state tests. In either case, the benefits of tutoring are going to be far more than simply getting better grades. When a student uses a tutor successfully, they are going to have higher self-esteem and they will likely have the confidence that is necessary to succeed in life. Make sure that you are taking full advantage of what a tutor has to offer to you during your school career.

Finally, consider the possibility that you are going to need additional help at some point during your schooling. We've already discussed the point of using a tutor but even if a tutor is not desired, you should still seek assistance when any problems display themselves. The sooner you get help for your problems, the more likely it is going to be that you will overcome those difficulties and really succeed. It will also benefit you by showing the teacher and anyone else involved that you are serious about your schooling and want to do your very best.

Ralph Gomez is the author of this article about maintaining better grades in school. Working as a counselor he has shown students many online resources to get tutoring for state tests . Another great resource to use are math tutors online for kids struggling with math. This advice has helped student maintain better grades in school.

Rubber Room Ruckus - Los Angeles Unified Policy Run Amok

It was more of thud then a knock and it shook me from the newspaper article I was reading. I should have ignored it; I already knew it was one of the kids who'd been kicking at my door during nutrition and lunch break when they're free to roam school grounds. My room was on the second floor balcony of one of many bungalows located on the southern edge of campus. These same kids had been making quite a commotion just outside my door for weeks on end as I tried vainly to shoo them away with appeals as well as threats. My requests to the main office for assistance always went unanswered.

But this time I decided to act quickly. I raced out and found one of the students standing there laughing at me. I was surprised to see her since they're usually in flight when the door flies open. This young lady was quite brazen; when I asked for her name she smirked and began walking away. That's when I reached out to her half heartedly; I knew I couldn't restrain her in order to get information, but I felt disrespected if I didn't do anything. So I reached out with my arm to show I meant business, but without the intention of grabbing her. My hand slightly touched her upper arm. She continued walking away and disappeared down the stairs. I didn't think anything of it until a few hours later when the Principal walked in to my room in the middle of a lesson and told me to take my things and immediately head over to her office; the police wanted to speak with me.

I spent an hour going back and forth with the two officers about who did what and when. They told me the student claimed I assaulted her and that my actions could be considered child abuse. They're methods were intimidating. I was treated as if I was guilty until proven innocent. They kept repeating the term 'child abuse' and even mentioned incarceration when I asked how serious the charges were. Eventually they left the room and I ended up the day talking to my union rep. She told me they could not have arrested me for what had happened; their intimidation was only a tactic. I wondered if those policemen gave the student the same treatment I got.

The next day I was told to gather my belongings from the classroom and return all room keys to the administrator. They were putting me on administrative leave; I was told to show up at the District office in Van Nuys where I would spend my days in a room filled with other teachers who were in the same boat.

The swiftness of the District's actions and the decidedly abstruse way they dealt with it was quite a shock to me. I never thought that a minor run-in with a student could lead to such punitive action. There are hundreds of other 'rehoused' teachers sitting out the day in so called rubber rooms, many of whom don't even know the allegations against them.

There's a witch hunt going on right now, and the judge and jury has a name and address - John Deasy, Superintendent of schools, LAUSD. This man has been intent on getting rid of classroom teachers for the past two years since becoming Superintendent. He initiated this stalinesque course of action, and he is ruining the lives of good teachers as well as students left dangling in their studies and school work when we're ripped out of the classroom in such a manner.

The District has enough work on their hands improving academics and student performance; they need to stop the charade of hiding behind abstract goals of student safety in order to thin the ranks of teachers for their own purposes.

Get rid of pedophiles, not credentialed school teachers who are just doing their job.

Solving Geometry Angles Problems

Introduction solving geometry angles problems:

Geometry is the most important branch in math. It involves study of shapes. It also includes plane geometry, solid geometry, and spherical geometry. Plane geometry involves line segments, circles and triangles. Solid geometry includes planes, solid figures, and geometric shapes. Spherical geometry includes all spherical shapes. Line segment is the basic in geometry. There are many 2D, 3D shapes.2D shapes are rectangle, square, rhombus etc. 3D sahpes are Cube, Cuboid and pyramid and so on. Basic types of angles are complementary angles and supplementary and corresponding , vertical .

Basic Geometric Properties used in solving problems

Some important theorems used in solving geometry problems :

The sum of the complementary is always 90 degree.

The sum of the supplementary is always 180 degree.

When two parallel lines crossed by the transversal the corresponding angles are formed. Those angles are equal in measure.

When two lines are intersecting then the vertical are always equal.

In a parallelogram the sum of the adjacent are 180 degree. And the opposite are equal in measure.

Solving example of geometry problems

Solving geometry problems using the above properties :

Pro 1. One of the given angles is 50. Solve its complementary angle.

Solution:A sum of complementary angle is 90 degree.

Given angle is 50

So the another angle = 90-50

So the next angle = 40

Pro 2. One of the given angles is 120. Solve its supplementary angle.

Solution: A Sum of supplementary is 180 degrees

Given angle is 120 degrees.

So, the unknown = 180-120.

So,the unknown = 60 degrees.

Pro 3. The angle given is 180.Solve its corresponding .

Solution:Corresponding are equal

So, the answer is 180

Pro 4. A figure has an of 45 degrees. Solve its vertically opposite angle.

Solution:Vertically opposite are equal.

So, the answer is 45 degrees.

Pro 5. One of the two of the triangle is 55 and 120 degree. Solve the measure of third angle

Solution:Sum of = 180 degrees.

So, the third = 180 - (55 + 120)

= 180 - 175

= 5 degrees

So, third angle is 5 degrees.

Pro 6. If one angle of the parallelogram is 60 degree. Solve the other three .

Solution:A sum of the in a parallelogram is 360 degree.

In a parallelogram adjacent angle are supplementary and opposite are equal.

Therefore, opposite angle of 60 degree is also 60 degree.

And the adjacent angle of 60 degree is 180 - 60 =120 degree.

Here, other three angle are 60 degree and 120 degree, 120 degree.

Trend of Day Care Services and Center For Kids in India

The growing inflation rate in India has created the need for both parents to do job and generate income for family. As a result of this parents who are usually working for long hours are unable to spend sufficient time with their child to teach them at-least basics of life such as numbers, alphabets, ability to identify pictures of fruits and vegetables, etc. Because of this, parents leave their kids in day care homes. The market trend of child care is moving away from solely babysitting child to child development care due to busyness and tight schedule of parents. Today's working parents need a service provider who not only provide care to kids in their absence but also help them in development of their kids along with safety features, thus, they are turning towards childcare services offered by number of kids school.

This will also benefit the toddler care houses because today, their state-of-the-art learning systems aid them in offering child care services as well as support them in nurturing child development. These day care schools provide caring services rather than normal school hours to kids wherein they learn and play at the same time. Nowadays, there are a number of kid's schools are offering child care services to toddlers aged two to five. Moreover, there are also some child care schools that provide accommodation and child care services to kids aged less than two.

After Mumbai, Delhi and NCR is the biggest region of India where majority is of emigrated people who come from all over the country and form nuclear family structure here. As in most of the families both the parents are working, they search for play school in delhi for their kids that can provide facilities that would help their kids to live there with ease in an safe environment. Delhi kids school or Delhi play schools presents an innovative solution as they present themselves as virtual parents and broadening the infants and children skills during the day.

The pre nursery school Delhi have geared up themselves with advanced educational toys and other educational playing goods which help schools engaging kids throughout the day in learning new skills. The elements that make Delhi preschool to rely upon them are as follows:

Superior customer attentionImmaculate care of the childrenProfessionalismSafetyState of the art learning systemLow teacher to student ratioCustom made facilities, and innovative learning programs

Extreme Value Analysis

Extreme value analysis is the branch of mathematics that deals with finding the maximum & minimum of a function. There are different ways to do that; the easiest being that by calculus. One of the other methods are by completing the square but that analysis can only be done in certain specific kinds of functions, quadratic functions to be specific. Many a times mathematics or in that case any branch of science requires finding out the limits(upper or lower) of a function to determine different properties of the function thereof. That's when we need to do the extreme value analysis to suit our needs.

Analytical definition for extreme value analysis

A function f(x) is said to have a local extremum point at the point x*, if there exists some e greater than 0 such that f(x*) greater than or equal to f(x) (for maxima) or if f(x*) less than or equal to f(x) (for minima) when |x - x*| less than e, in a given domain of x. The value of the function at this point is called extremum of the function.

A function f(x) has a global (or absolute) extremum point at x* if f(x*) greater than or equal to f(x) (for maxima) or if f(x*) less than or equal to f(x) (for minima) for all x throughout the function domain.

Tests: for extreme value analysis

There are two tests in calculus to for extreme value analysis, the first derivative test and the second derivative test. First of all, the extreme values occur at the critical points of a function, i.e., wherever the slope of the function is 'zero' or 'not defined'. Then, to check whether these points are actually extremes and also the kind of extremum i.e., whether it is a maximum or a minimum is given by the aforesaid tests. While the first derivative test gives us the kinds of the extreme points by analyzing, manually, the change in the sign of the slope of the function before and after the respective point, the second derivative test directly gives us whether a point is maximum or minimum by simply noticing the sign of the second derivative of the function at the respective point.

Extreme value analysis : A quick glance

Suppose that x* is a critical point at which f'(x*) = 0.

(i) First Derivative Test :

If f'(x) greater than0 on an open interval extending left from x* and f'(x) less than0 on an open interval extending right from x*, then f(x) has a relative maxima at x*.

If f'(x) less than0 on an open interval extending left from x* and f'(x) greater than0 on an open interval extending right from x*, then f(x) has a relative minima at x*.

If f'(x) has the same sign on both an open interval extending left from x* and an open interval extending right from x*, then f(x) does not have a relative extreme at x*.

(ii) The Second Derivative Test :

f(x) has a relative maxima at x*if f''(x*) less than0.

f(x) has a relative minima at x* if f''(x*)greater than0.

f(x) does not have any extreme values at x* if f''(x) = 0.

Q: Show that if the sum of two numbers is constant, their product will be maximum if the two numbers are equal!

A: Let the numbers be x & y, so that, x - y = c (constant)

Now, let M = xy

= M(x) = x(x-c)

= M'(x) = 2x - c

= M''(x) = c less than 0 [ so M'(x)=0 will give a maxima]

so, putting M'(x) = 0 [condition for maxima exam]

= 2x - c = 0

= x = c/2

Therefore, y = x - c = y = c/2 ;

This shows, that the product (M) is maximum when x = y!!!

Learn more on about Perimeter of Trapezoid and its Examples. Between, if you have problem on these topics Rounded Rectangle , keep checking my articles i will try to help you. Please share your comments.

Activities at Mommy and Me Classes

Mommy and me classes are very helpful for both the mother and her infant or toddler since it brings them much closer to each other. At the present time this social classes are very famous all over the world. The mommy and me Calabasas are found in several diverse places of this country. Not only that in fact mommy and me classes Agoura Hills and Hidden Hills are also very famous and a lot of people are very much fond of it. Many time people ask why such a class is so important to join. Well basically there are endless benefits of such mommy and me class. Let us have a look at its advantages that are lined up below.

It strengthens the bonding between the mother and the child: As already said that the mommy and me classes are a great way to strengthen the bond between the child and the mother. Both get a quality time to spend with each other and this provides them a sense of safety and optimistic self value. Since in this type of a class both the mother and kid interact with each other the most and take part in a single activity together the bond get stronger and flourish.It helps the child to develop the communication and social skill: In these special classes the mommies get chance to develop the social awareness and communication skill of their child. For children who are introvert or timid this type of a class can make a lot of changes. Other than that in such classes the children also get the scope of leveraging their skill of understanding, self control and much more. In fact in some cases it is found that they start learning new things themselves and they start being creative which is a great thing about the children.Great way to make friends: Since in these classes you kid gets the chance to meet a lot more buddies of his age or of different age along with their moms it helps him or her lot make out his best buddy out of the crowd. Friendship is a must need of motherhood, these classes gifts the key of that actually.Lighten the loneliness: If the parents are working the children often feel lonely and they cannot share their loneliness. But if they get chance to spends a single day with their mother through this class it lessens their feeling of loneliness in large extend.Prepares child for school: The mommy and me classes can be termed as a preschool session as well as this contributes a lot in their academics and nursery school.

Other than these classes the children learn to set up with diverse situation, they learn how to figure out and solve problems; they learn to follow directions and much more that point out a good start o their educational and social life. As a whole this is actually a very helpful session for both the mothers and their children.

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Andrew Michael Joseph has published 5 articles. Article submitted on May 27, 2013. Word count: 493

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Help With Third Grade Math

Introduction to help with third grade math:

Study of basic arithmetic operations and arithmetic functions is called mathematics. Help with third grade math used to learn some basic math operation. In mathematics, basic concept is arithmetic operations.

The basic arithmetic operations are addition, subtraction, division, multiplication and placing values. The help with third grade math is deals with basic algebra and involves a basic math operation only. In this article we are discussing about help with third grade math.

Examples problems for help with third grade math:

Basic addition problems for help with third grade math:

1. Find the add value of the given nos, using addition operation, 322 + 415 + 208

Solution:

Given nos using addition operation for, 322 + 415 + 208

First step, we are going to add the first two nos,

322 + 415 = 737

Then add third number with first two nos of sum values,

737+ 208 = 945

Finally we get the answer for given nos are 945.

2. Find the add value of the given nos, using addition operation, 907 + 549 + 284

Solution:

Given nos using addition operation for, 907 + 549 + 284

First step, we are going to add the first two numbers,

907 + 549 = 1456

Then add third number with first two numbers of sum values,

1456 + 284 = 1740

Finally we get the answer for given numbers are 1740.

Basic subtraction problems for help with third grade math:

1. Find the subtract value of the given numbers, using subtraction operation, 840 - 453 - 385

Solution:

Given numbers using subtraction operation for, 840 - 453 - 385

First step, we are going to add the first two numbers,

840 - 453 = 387

Then subtract third number with first two nos of subtracted values,

387 - 385 = 2

Finally we get the answer for given numbers are 2.

2. Find the subtract value of the given numbers, using subtraction operation, -278 + 452 - 603

Solution:

Given numbers using subtraction operation for, -278 + 452 - 603

First step, we are going to add the first two numbers,

-278 + 452 = 174

Then subtract third number with first two numbers of subtracted values,

174 - 603 = -429

Finally we get the answer for given nos are -429.

Basic multiplication problems for help with third grade math:

1. Find the multiply value of the given nos, using multiplication operation, 45 * 31 * 2.

Solution:

Given nos using multiplication operation for, 45 * 31 * 2

First step, we are going to multiply the first two nos,

45 * 31 = 1395

Then multiply the third number with first two nos of multiplied values,

1395 * 2 = 2790

Finally we get the answer for given numbers are 2790.

2. Find the multiply value of the given numbers, using multiplication operation, 11 * 5 * 10

Solution:

Given numbers using multiplication operation for, 1 * 5 * 1

First step, we are going to multiply the first two numbers,

11 * 5 = 55

Then multiply the third number with first two numbers of multiplied values,

55 * 10 = 550

Finally we get the answer for given numbers are 550.

Introduction to Measurement

Introduction to measurement:

A physical quantity can not be understood completely by a simple description of its properties. While describing a person, we call him short or tall or heavy or light. This will not give full description of the person. We must have quantitative measurement of his height or weight, i.e., the physical quantities. There is an immense need to measure relevant physical quantities to have a comprehensive understanding of related physical phenomena. Lord Kelvin felt that the knowledge of physical quantities accurately and express them in numbers. Without measurements there can be no development in physics. The experimental measurements are highly essential to verify the theoretical laws. In our daily life we use a number of physical quantities like length , time , area, volume , speed, velocity, acceleration, force temperature etc. For measuring a physical quantity, a standard reference of the same physical quantity is essential. This standard reference is called 'Unit'.

Introduction to Measurement:: Centimeter and meter

A unit of measurement of a physical quantity is the standard reference of the same physical quantity which is used for comparison of he given quantity. In any measurement of a quantity, the final result is expressed as a number followed by the unit. For example, the height of a person is 1.6 metres. Here 'metre' is the unit and his height is expressed as 1.6 times (a number) multiplied by the unit. It can also be expressed as 160 centimetres, where 'centimetre' is the unit. The smaller the unit, the greater is the number of times that unit is contained in the quantity. Hence depending on the situation, suitable units have to be used to measure the quantities. The unit must be accepted internationally. A standard unit should be consistent , reproducible, invariable and easily available for usage. The process of measurement of a quantity involves : (a) Selection of a unit (b) to find the number of times that unit is contained in the physical quantity.

Introduction to Measurement::Significant measures

As precise and accurate measurements of physical quantities are quite essential in the study of physical sciences, measurements forms the basic foundation of any scientific investigation. There will be certain amount of uncertainty inherent in the measurement of quantities by any instrument. This uncertainty is called the 'error' . Basing on measured values of the quantity, we make certain calculations like addition, subtraction, multiplication and division. For example, we divide the distance travelled by an object by the time taken to find the speed of the object. Such calculations will also contain the errors in the measurements.

Certain (minimum number of ) quantities like length, mass, time, ...etc , are taken as the fundamental (base) quantities and are represented by capital letters as L, M, T, ..etc. Any other quantity can be expressed as a product of different powers of these fundamental (base) quantities. In such an expression, the power of a fundamental (base) quantity is called the dimension of that quantity in that base. For example, velocity can be expressed as displacement / time = '(L)/(T)' = L1-1 . Hence, the dimensions of velocity are in 1 in length and -1 in time. T

As every measurement contains errors, the result of a measurement is to be reported in such a manner to indicate the precision of measurement. We report the result of the measurement in the form of a number along with units of the quantity concerned. The number should be such that it includes all the digits that are known reliably and in addition one more digit that is an estimation and is not quite certain or reliable. The reliable digits plus the uncertain digit are called the 'Significant digits' or 'Significant figures' .

7 Things That Make Matrikiran The Best Option

MatriKiran is an English medium, co-educational school for grades Pre-Nursery to 12. Auro Education Society, the education arm of the Vatika Group, manages it. It is an 8-acre campus expanded over two locations: the primary wing at Sohna road spread over 2 acres, and middle and senior wings at Vatika INXT spread across 6 acres. The corporal, psychological, emotional, intuitive, and religious facets of the growth are all catered through learning by study and innovation.

"Child is like wet cement. Be careful what impressions you leave," rightly said. We believe every child is special and needs proper attention. The wings of imagination should never be burdened by expectations. Every child deserves to be happy, educated, and future ready.

7 things worth noting are:

1. Faculty

"Those who educate children well are more to be honored than they who produce them; for these only gave them life, those arts of living well." - Aristotle.

The quotation tells you the importance of a teacher. We at Matrikiran, have caring, experienced, and qualified members who are literate in integral education to contribute towards the overall development of each student. Innovation is the key to survival. Constant innovation and creation of learning experience is incorporated in order make learning an easy process for students. Education by Vatika has always been up to the standards.

2. Infrastructure

Education is not only about classrooms. The process really matters. The spaces suggest visual, audio, kinesthetic, and method skills, necessary for values of education.

3. Locker room facilities

All students have been provided with locker room facilities to keep their belongings safe.

4. Library

The library stores enormous collection of 15000 volumes. Library enthusiasts can sit, learn and acquire loads of knowledge.

5. Laboratories

It is important for students to learn and experience the theoretical facet of a subject. Laboratories have been provided with qualified staff members to assist. Experienced faculties guide the students through the experiments. Laboratories for Biology, Physics, Chemistry, Biotechnology, Geography, Environmental science, Mathematics, and Home science have been incorporated with ample space for the students to perform the experiments.

6. Auditorium

An auditorium is used for functions and annual meets. It is big enough to hold a large number of audiences.

7. Location

It is believed that schools be located in a quiet and secure environment. One of the Best Schools in Gurgaon is located in Vatika INXT. Vatika INXT is located at the juncture of NH8 and Dwarka expressway.

Matrikiran is one of the premier preparatory schools in Gurgaon which has set up its standard and are striving hard to live up to the expectations of the people associated with them. For more information, visit: http://www.matrikiran.in/

Know How The Best Boarding School Can Contribute Positively to Your Child's Future

Every child is special. So, each of them should get equal opportunity which helps them in achieving his/her full potential. This is where the educational institution plays a significant role.

The modern concept of education is aimed at helping each student to grow up as a responsible and confident human being. There are international schools which recognize the fact that the teaching process becomes effective only by continued development and deployment of outstanding teaching faculty along with excellent curricular and co-curricular activities. This is further aided by efficient use of modern teaching tools and techniques.

The main advantage of opting for residential schools is that students remain under constant guidance of experienced faculties. Teachers not only assist the student in gaining mastery over the subject but also help in developing their communication and social skills. In fact, they play quite a significant role in shaping up the child's future. Thus it is very important that you opt for the best boarding school only. Given below are few criteria which will help in the search:-

The location of the school - is an important factor since your precious one is going to stay there for a long time, away from home. Usually parents prefer residential schools at convenient localities which are not difficult to commute. In general the school follows same syllabus of the country/state where it is located. However, international schools have their own distinct curriculum. If you have plans to send your child abroad then global schools can be a better option.The infrastructure and amenities offered by the school - should be verified properly, more so, if you are on the look-out for residential school. Do confirm if the school has proper hostel facilities, separate arrangement for boys and girls. You can request to have a look at the type of accommodations offered, just to verify if the rooms are spacious and comfortable enough.Faculties - should be qualified, sincere and patient enough to handle boarding school students. Since different types of students take admission, few of them difficult to handle too, responsibilities of teachers increase manifold. They should be there to guide students through tough subjects and monitor them constantly. They should also offer counseling from time to time, if any student needs so.Academics and extra-curricular activities - are equally important. The best boarding school designs these activities such a way that students don't feel stressed or over burdened. Apart from class room teaching, arrangements are made for audio-visual sessions which students find interesting. A range of extra-curricular activities are offered so that students can pick the one up as per their preferences.

When it comes to sending your child to the best boarding school, it is very important that you know the kid's opinion too. If your child shows unwillingness then do explain in details why such an education is important and how the residential school will contribute to a bright future. A best approach is to arrange a visit to the school so that the kid can have a first-hand idea of the school ambiance. Encourage him/ her to interact with boarders of same age group. At the same time, you can have a talk with the school administration officer, teachers or educators.

The author has written a number of interesting and informative online articles on how to select the best boarding school. Parents who are searching for residential schools will find these articles helpful. Rate this Article

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Manish Neelan has published 1 article. Article submitted on March 07, 2013. Word count: 535

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Types of Management Plans

Introduction:

The prosperity of an organization depends upon the preparation and execution of the management plans. It is a well known fact that it is impossible for an organization to operate without outlining proper management plans. Over the years through extensive study and management research, many scholars have divided management plans in two types, namely, Strategic Management Plans and Operational Management Plans.

Classification of management plans

Strategic Management Plans - It involves proper planning and far-sightedness for conceptualizing the strengths and weaknesses of the organization, pertaining to the environment in which it exists. Strategic Management Plans deals with the envisioning of at least three to five years in the future and deciding what are the pathways that the organization intends to take and create new vistas of opportunities. It strongly involves the basic elements of market research and financial projections with detailed study of promotional planning and taking all the necessary steps to fulfill the operational requirements. It is the best way to find out the amount of capital to be raised, expansion target and optimum use of the available resources. Strategic managerial plans also deals with relationship managerialas in today's world, management and the correct use of contacts is very important.

Operational Management Plans - It is the interim period which deals with Operational Management Plans. This is also termed as Tactical Planning and it also deals with the aspects that involve the concept of an annual budget. Operational managerialPlans entirely focuses on making sure that a given task is completed. It is irrespective of whether it is driven by the entire organization's budget, any personal budget or any functional area of responsibility. It can also be said that operational managerial plans are indirectly derived from strategic managerial plans. It is an outflow of a detailed strategic managerial plan and can be seen as a part of the initiating and implementation stage of a more comprehensive long term plan.

Standing & Single Use Management Plans -

Standing Plans are further of three types, namely Policies, Procedures and Rules. While Single Use Plans are further of two types, namely, Programs and Budgets. Here is a short note on different types of Standing and Single Use Plans :

Policies - It focuses on accomplishing the organization's objectives by furnishing the broad guidelines for the correct course of action.

Procedures -Procedures outline a more specific set of actions and deals with the implementation of a set of related actions in order to finish a particular task.

Rules - Rules are a set of guidelines that show the way and manner in which a task is to be accomplished. It lays down the do's and don'ts that are to be strictly followed by the members of the organization without any deviation.

Programs - Programs deal with the guidelines that are set for accomplishing a special project within the organization. The project may not be in existence for the entire tenure of the organization, but if the project is accomplished, it might result in short-term success of the organization which might ultimately prove to be extremely helpful.

Budget - A Budget represents a specific period of time which indicates it as a single user financial plan. It is a complete set up indicating the process of procuring the funds and channelizing the funds. It shows in details how funds are to be utilized on labor, raw materials, capital goods, marketing and information systems.

Online Basic Geometry Definitions

Introduction :

In this article online basic geometry definitions tutor,we will learn some important geometry definitions they are necessary to understand geometry concept.Those basic geometry definitions are used to design a graph with the assistance of those terms. Tutor will teach to individual and guide them to get the solution for problems through some websites via online. Online is a tool for self-learning from websites.

Basic definitions-

Supplementary angles:

We can call any two angles as supplementary angles,if the sum up of them should be 180°

Complementary angles:

We can call any two angles as complementary angles,if the sum up of them should be 90°

Acute triangle:

An acute triangle means a t in which all three angles should be less than 90°.

Obtuse triangle:

Obtuse triangle means one type of tria in this one angle must be greater than 90°.

Right angle triangle:

A right angle tria means one type of tri in which one angle must be a right (90°) angle.

Triangle Inequality:

The triangle inequality means the addition of any two side should be greater than the third side

Scalene Triangle:

A scalene trigle means a triangle with three different unequal length of side.

some more definitions-

Centroid:

The centroid means a point in which three lines will meet each other. This point is a center point of a trigle. If we cut a tria corresponds to that center we will get three equal parts.

Circle:

In circle the distance between the center and to any point present in the outer line of a circle is same.

Radius:

Radius of a circle is the distance between the circle's center and any point present on the circle.

Circumcenter:

In a triae three perpendicular line drawn from the three sides bisect each other . That point is called as circumcenter.From this center point we can draw a circle

Congruent:

Two figures are said to congruent when all the parameters should be same interms of length and angles.

Altitude:

An altitude means a line connecting a vertex to the opposite side.

Vertex:

Vertex means a point.

Transversal:

A transversal means a line which passes through two another lines there is a no issue that should be parallel.

Point:

A point indicates a single location

Plane:

Plane is a flat, two-dimensional object one.

Quadrilateral:

Quadrilateral is defined as a polygon and has exactly 4 sides.

Trapezoid:

A trapezoid means a quadrilateral which contain one pair of opposite side they should be parallel to each other.

Polygon:

A polygon means a two-dimensional geometric object.It is made up of a straight line segment those segments touches at the ends.

Rectangle:

Rectangle means a quadrilateral and should has 4 right angle.

These are the few terms for basic geometry

Number of Divisors

Introduction to Whole Number Divisors:

A division method can be done by using the division symbol ÷. The division can be otherwise said to be inverse of multiplication. The one of the major operation in mathematics is division operation. In division, a ÷ b = c, in that representation "a" is said to be dividend and "b" is said to be divisor and "c" is said to be quotient. The letter "c" represents the division of a by b. Here the resultant answer "c' is said to be quotient. Let us see about whole number divisors in this article.

Whole Number Divisors for the Number eighty

The numbers that can divide by eighty is said to be the divisors of eighty.

Let us assume that eighty can be divided by 2, 4, 5, 8, and 10.

Example 1:

Divide the whole number 80 ÷ 2

Solution:

Let us write the given number eighty inside the division bracket. The divisor can be put it in the left side of the division bracket.

2)80(

The number 2 should go into 8 for 4 times. So, put 4 in the right side of the bracket.

2)80(40

8

---------------

00

00

-------------------

The zero can be placed just near the 4 in the quotient place.

The solution for dividing eighty by 2 is 40.

Example 2:

Divide the whole number 80 ÷ 4

Solution:

Let us write the given number eighty inside the division bracket. The divisor can be put it in the left side of the division bracket.

4)80(

The number 4 should go into 8 for 2 times. So, put 2 in the right side of the bracket.

4)80(20

8

---------------

00

00

-------------------

The zero can be placed just near the 2 in the quotient place.

The solution for dividing eighty by 4 is 20.

More Problems to Practice for Finding the Divisors for eighty

Example 3:

Divide the whole number eighty ÷ 5

Solution:

Let us write the given number eighty inside the division bracket. The divisor can be put it in the left side of the division bracket.

5)80(

The number 5 should go into 8 for 1 time. So, put 1 on the right side of the division bracket.

5)80(1

5

---------------

30

-------------------

Then the number 5 should go into 30 for 6 times. So put 6 just near the 1 on the quotient place.

5)80(16

5

---------------

30

30

----------------

0

----------------

The solution for dividing 80 by 5 is 16.

Example 4:

Divide the whole number 80 ÷ 8

Solution:

Let us write the given number eighty inside the division bracket. The divisor can be put it in the left side of the division bracket.

10)80(

The number 8 should go into 8 for 1 time. So put 1 on the right side of the division bracket.

8)80(10

8

---------------

00

----------------

The zero can be placed just near the 1 in the quotient place.

The solution for dividing eighty by 8 is 10.

Example 5:

Divide 80 ÷ 10

Solution:

Let us write the given number eighty inside the division bracket. The divisor can be put it in the left side of the division bracket.

10)80(

The number 10 should go into 8 for 0 times. So, take the digit as two digits in a given number of the division bracket.

Then the number 10 should go into eighty for 8 times. So put 8 on the right side of the division bracket.

10)80(8

80

---------------

0

-------------------

The solution for dividing eighty by 10 is 8.

Therefore, the divisors for the whole number eighty are 2, 4, 5, 8 and 10.